Year 1 Sem 1/LC Optics and Waves/Lecture 01

Lecture 1: Intro to Waves and SHM Recap
Wed 01 Oct 2025 11:00

Course Objectives

Have a sound understanding of basic wave properties
Have a basic understanding of interference effects, inc diffraction
Be able to use simple geometric optics and understand the fundamentals of optical instruments.

Periodic Motion

Waves are very linked to periodic motion. Therefore we recap periodic motion first.

It has these characteristics:

A period, $T$ (the time for one cycle)
A frequency, $f$, the number of cycles per unit time ($f = \frac{1}{T}$)
An amplitude, $A$, the maximum displacement from equilibrium.

Periodic motion continues due to the restoring force. When an object is displaced from equilibrium, the restoring force acts back towards the equi point. The object reaches equi with a non-zero speed, so the motion continues past the equi point and continues forever.

Energy

Periodic motion is an exchange between potential and kinetic energy, with no energy loss. Energy is conserved.

Simple Harmonic Motion

If the restoring force is directly proportional to the displacement $F = -kx$, then the periodic motion becomes Simple Harmonic Motion and the object is called a harmonic oscillator.

In a single dimension, displacement is given by:

$$x = A \cos(\omega t + \phi)$$

Where $\omega = 2 \pi f$ is the angular velocity, and $\phi$ is the phase angle. In cases like this, where the phase angle is $90 \deg$ we can simplify to $x = -A \sin(\omega t)$

More SHM Equations

Velocity

$$v_x = \frac{dx}{dt} = - \omega A \sin(\omega t + \phi)$$

Acceleration

$$a_x = \frac{d v_x}{dt} = \frac{d^2 x}{dt^2} = - \omega^2 A \cos(\omega t + \phi)$$

Both properties are signed to indicate direction, as they are both vectors.

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